By "nobility" I take it that you mean the hereditary peers who were disqualified from sitting in the House of Lords by the 1999 House of Lords Act.
These hereditary peers have no special legal status. They can vote and seek election to the House of Commons. Indeed there were (as of 2008) three members of the nobility elected as MPs, John Thurso and Michael Ancram and Douglas Hogg, though all three have since left the Commons. John Thurso and Michael Ancram have been made life peers, and so now can sit in the Lords. John Thurso was the only one of the three to have been a hereditary peer in 1999, and so the only person to have moved from the Lords to the Commons, then back to the Lords.
Prior to the 1999 act, Lords could renounce their nobility in order to stand for election to the Commons. This right was given in 1963, and used by Tony Benn, Quentin Hogg and Alec Douglas-Home to become MPs.
"Lord" Buckethead, and Screamin' Lord Sutch have never been disqualified from running. In both cases "Lord" is part of their nickname.